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Thank You all!!!

1.   Notice, NSS...that p  cannot  =  - 4  because the denominator would be  =   0

Factoring   p^2  - 4p  - 32   we get  ( p + 4) ( p - 8)

This would give us

[ (p + 4) ( p - 8) ]  / (p + 4)     the (p+4) 's   cancel

So we're left with   p - 8

So...the second answer is correct

2.   [ q^2  + 11q   + 24 ]  / [ q^2 - 5q - 24 ]      factor top/bottom

[ (q + 8) (q + 3) ]  / [ (q - 8) (q + 3) ]

Notice that   q cannot equal  either 8 or -3 because these would make the original denominator = 0

Now.... the  (q + 8)   factors "cancel on  top/botom   and we're left with  

(q +8 ) / ( q - 8)

So....the thiird answer is correct

Here's one way of doing this

Cos (90 - x)  =  √3/2

Notice that  

Cos (30°)    = √3/2

So.....x must be  = 60°

So.....sin (60°)  = √3 / 2    !!!!!

Does that make sense, RP???

Thanks, CPhill! 

We want to choose 1 girl out of the 24 and 1 boy out of 12

So.....the total number of ways to do this is :

C(24,1)  * C(12, 1)  =   24 * 12  =    288 ways

Good job, RP and tertre....!!!!!

Oh wow, I honestly didn't even realize that. Thanks~

Notice RP, that p, q, r, s, t, u  are all equal to 45°.....so their sines and cosines are all equal....so all the statements are true  !!!

Good job, RainbowPanda!

x is not 5.....

First, we can apply the radical rule, to get \(\sqrt{-1}\sqrt{9}\) . Then we can apply the imaginary rule, to get \(\sqrt{9} i=3i\) . Doing the same thing with, \(\sqrt{-36}\), we get \(6i\) . So, \(3i+6i=\boxed{9i}\)

√-9 + √-36

For √-9, apply the radical rule: √-9=√-1√-9

Apply imaginary number rule which is √-1=i

So √-9i

√9=3, so now we have 3i

Now for √-36, apply the radical rule first: √-36=√-1√36

(Imaginary number step) We have √-36i now.

√36=6

So we have 6i

We ended up with 3i+6i which is equal to 9i, and that's your answer.

GCD{a, 50} = x + 5

LCM{a, 50} =x(x + 5)

One simple solution is:

a = 10, and x = 5, since:

GCD{10, 50} =10, and x + 5 = 10, therefore x=5

LCM{10, 50} =50, and x(x + 5) = 50 =x^2 + 5x, therefore x = 5

Thanks All of you

Vertex form of a parabola :

y = a(x-h)^2 +k

First one:    y = a (x-4)^2 -2     You are given a convenient point on the parabola to find 'a'

Let's sub 7,3  into the equation

3 = a (7-4)^2 -2      solve for a = 5/9

y = 5/9 (x-4)^2 -2  

Hey, Manuel!

We can first subtract \(-8+y\) from both sides, to get \(\sqrt{y^2}-8+y-(-8+y)=4-(-8+y), \sqrt{y^2}=-y+12\). After that, we can square both sides, expand, and expand again, to get \(y^2=y^2-24y+144\) . Solve, to get \(y=6\)

Let's start off by Subtracting -8+y from each side which would now make this: √y^2 - 8 + y=4 into this: √y^2=-y+12

(I'm horrible at explaining things, sorry!)

Now we square both sides, (√y^2)^2=(-y+12)^2

First let's do (√y^2)^2 

√y=y^1/2 so let's replace the square root with 1/2 now we have (y^2 and 1/2)^2

Let's apply the exponent rule: (a^b)^c=a^bc which makes us have y^2 and 1/2*2 which makes it A LOT easier to solve this problem. 1/2*2=1

1*2/2=2/2=1, we end up with y^2

Now we have to solve (-y+12)^2

Apply the distributing rule: (a+b)^2=a^2+2ab+b^2 (a=-y and b=12)

We now have (-y)^2 +2(-y)*12+12^2 (SIMPLIFY)

Remove the parenthesis. y^2 -2y*12+12^2

(-a)^n=a^n (only if n is even)

(-y^2)=y^2

y^2-2*12y+12^2

Refine: y^2-24y+144

Now we have y^2=y^2-24y+144, so we have to solve that now. 

Subtract y^2 from both sides and we get: 0=-24y+144

Let's subtract 144 from both sides which= -24y=-144

Divide both sides by -24: -24y/-24=y and -144/-24=6

So, y=6

I just made it really confusing xD but yeah that's it.

Complimentary angles ADD to 90 degrees.

     then   A+B=90      so   B= 90-A

    SO the FIRST choice is obviously true!   (and the last choice is NOT true (except at 45 degrees))

The second and third are basically the same statement.  (they are both true)   

   Draw a right triangle    one angle is 90 degrees   the other angles total 90 degrees (A and B)

     Now look at this diagram:    For any right triangle you can draw (which means A and B add to 90 degrees)     You can see that for compimentary angles  cos A = Sin B

Here is my sketch:

Since it is an isoc right triangle the two legs are the same length (and the angles of the triangle are 90 45 45)       Line DC = 5    Line BD = 5    AND Line AD will equal 5   

Area of smaller triangle = 1/2 (5)(5)        Total area will be the sum of the two small triangles (which are identical)    2 x 1/2 5 x 5 = 25 units^2

Thanks a ton!

I understand a lot better now!

Thank you so much for all you guys do. It is so helpful for us students.

Have a great day!

For the THIRD one....    ADD the x and y's of a and g....do the sketch, then do the math the same way with the results of adding  these values !   Easy Peasy ! (once you catch on)

When they give you an x,y magnitudes, you are loking for the resultant HYPOTENUSE of a right triangle....first sketch the x and the y components, then use the pythagorean theorm to find the hypotenuse...

First one    x magnitude =6    y magnitude = -10     hypotenuse = sqrt(6^2 + 10^2) = 11.66

   the angle will be in the FOURTH quadrant (because y is negative)

     and is equal to arctan (-10/6) =  -59 degrees

Do you see how it is done? Try the second one!

I am sorry... I have no clue as to the answer of your question, but I just had to tell you...

SAERAN CHOI.

"I am you and you are me."

I'm more of a Saeyoung, myself, but I really really appreciate your profile pic. LOLOLOL!